Operations Research

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Operations Research

Overview

Operations research is, by its very nature, a multidisciplinary field in which a group of experts attempts to manage and optimize complex undertakings. These undertakings can be military operations, industrial systems management, governmental operations, or commercial ventures. The heart of operations research is the mathematical modeling of part or all of these ventures, which can provide more insight into the interactions of certain variables of interest. The technique of linear programming was developed, in part, to help solve some of these problems. Operations research proved invaluable in solving some military problems in World War II and in subsequent wars and has had a significant impact on the way complex operations are planned and managed.

Background

With the Industrial Revolution in the nineteenth century, production systems became more automated and mechanized, many activities became more complex, and people began to supervise and manage machines that produced goods. This led to the field of industrial engineering, in which designers tried to make machines and production lines as efficient as possible to maximize overall efficiency and corporate profitability.

During World War II, problems arose that required new methods to reach a satisfactory solution. One of these problems was finding German submarines in the open ocean; another was maximizing the utility of Britain's early radar warning networks; yet another was planning complex operations such as the invasion of Normandy. Each of these was exceedingly complex and required the integration of several specialties. In addition, it turned out that each of these problems could be solved, in part, using mathematical analysis to arrive at an optimum solution. Put more succinctly, operations research involves the scientific and mathematical examination of systems and processes to make the most effective use possible of personnel and machines.

Please note that, in this context, "optimum" does not necessarily mean "ideal"; it simply means the best solution possible given the constraints under which the problem is solved. For example, when all is taken into account, the optimum amount of time in which to move three divisions of soldiers and all of their equipment from the United States to the Middle East might be three weeks or to move only the soldiers in two days. If the soldiers and their equipment are required in three days, the "optimum" solutions to this problem are hardly what the planners would desire, but they are the best ones possible, given certain factors such as the number of transport planes available, the number of soldiers and equipment that can fit into a single transport plane, the number and length of runways for both takeoff and landing, the loading and unloading capacity at all airports involved in the mobilization, the amount of fuel available on short notice, the airspeed of the aircraft, the availability of aircrews to load and fly the planes, and many other factors.

It was quickly noted that many operations research problems are very complex. In theory, a large number of these problems cannot be solved easily because the number of possibilities increases exponentially with the number of factors to consider. In actuality, however, many possibilities can be disregarded because, although mathematically valid, they are not considered in real life. For example, in trying to find the optimum routing for supplies from a variety of production locations to a central shipping location, it is mathematically valid to consider shipping supplies from one location to that same location, although in real life this would not be done. Similarly, it is not reasonable to assume that an attacking airplane will originate its flight from over friendly territory, so attack vectors that originate behind friendly lines may be disregarded in planning an air defense system. These and other similar possibilities may be disregarded when setting up such a problem, simplifying it to the point of being solvable.

The inaugural use of operations research came in the late 1930s when future Nobel laureate P.M.S. Blackett (1897-1974) was asked to develop a way to make best use of new radar gunsights for anti-aircraft guns being introduced to the British air defense system. Blackett assembled a team that included physiologists, physicists, mathematicians, an astronomer, an army officer, and a surveyor. Each person brought unique insights and job skills to the task, collectively reaching a solution in a relatively short period of time. This success was noticed quickly by other branches of the British military and by the Americans, all of whom adopted operations research by the early 1940s. Other problems addressed in this manner included hunting submarines in the Atlantic Ocean, designing the mining blockade in Japan's Inland Sea, and helping to plan many major amphibious operations during the war.

After the end of the war, operations research was also adopted by many American businesses, correctly seeing this as a powerful tool that could be adapted to nonmilitary use. In the business world, operations research helped design efficient flow paths for parts being incorporated into a final product, designed transportation systems, and optimized electrical distribution systems. At this time, too, the first mainframe computers were being built, giving researchers new capabilities. More sophisticated models were made possible by high-speed computers and the use of linear programming (a mathematical technique in which operations are described in equations in which no variables are raised to exponential powers or are multiplied together). Provided a system could be described in mathematically simple terms without losing touch with reality, linear programming made it possible to solve problems exactly, rather than by guesswork and experimentation.

Two milestones in the field of linear programming were the development of the technique by Soviet mathematician Leonid Kantorovich and the discovery of "polynomial-time" algorithms for many problems by another Soviet mathematician, Leonid Khachian. Both of these breakthroughs made the solution to many previously intractable problems possible. Linear programming is used to construct an equation that describes the interactions of various aspects of a problem, such as the military mobilization problem mentioned above. For example, if the number of men (n_m) that can be transported in a single plane is 200 and five planes (n_p) are available, then no more than 1,000 men can be transported at a single time. If the time (t_l) to load a plane, fly to the destination, unload it, refuel, and return to the point of origin is 18 hours, then in three days (t_t), the number of men that could be moved is equal to:

In addition, certain inequalities will be set up as constraints on the problem. For example, a plane cannot hold more than 200 people, so we can say that n_m = 200. By programming a computer to solve all of these equations simultaneously while recognizing the inequalities, such problems can be "solved" by coming up with approaches that make the best possible use of available resources to reach a desired goal. Similar, albeit more complex analyses can be used to determine the best trade-off in this example, suggesting how to get the highest number of fully armed soldiers on the ground in the shortest period of time.

Impact

Operations research had an immdediate effect on the military success of Allied forces in the Second World War. While the Allies are likely to have won the war in any case, these techniques probably helped shorten the war and allowed it to be won on more favorable terms with fewer casualties. The same is true for subsequent wars, including the Persian Gulf War. In fact, operations research is increasingly important to the U.S. military in an era of declining enlistment, decreasing numbers of planes, ships, and tanks, and more complex military problems in a wider variety of scenarios. This combination requires the most careful possible planning to meet both national priorities and military obligations around the world.

Operations research has also influenced business and industry, giving companies the ability to analyze their operations for the most efficient use of personnel, transportation systems, and production systems. This, in turn, has increased productivity, reduced the use of resources, and streamlined operations, adding to profitability and corporate efficiency. Thes techniques have also been used by government organizations to increase efficiency in many areas.

Finally, in the area of science, operations research was perhaps the first truly interdisciplinary field of inquiry. As such, it not only pioneered many of mathematical techniques now used in other fields, but also helped pave the way for the current increase in interdisciplinary research. Assembling scientists from different specialties offers many different views of a problem and provides a wider variety of intellectual tools that can be brought to a solution. In a way, it is the equivalent of parallax: looking at an object from different vantage points to fix its position in space. This "intellectual parallax" not only gives scientists a better overall view of a problem, but allows the team a much better chance of reaching a solution because they can more quickly and more accurately outline the problem's boundaries.

P. ANDREW KARAM